# Rotator

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## rotator

[′rō‚tād·ər]## Rotator

a mechanical system consisting of a material point of mass *μ* held by a weightless fixed pivot at a constant distance *r* from a point O, which is fixed in space and constitutes the center of the rotator.

In classical mechanics, the permitted motion of the rotator is the rotation around the point *O* with a moment of inertia 7 *= μr ^{2}*. The motion of the rotator occurs in the plane perpendicular to the vector of the angular momentum

*M*of the rotator. The energy of the rotator

*E = M*

^{2}.

In quantum mechanics, the states of rotators are characterized by certain discrete values of the square of the orbital angular momentum *M*_{l}^{2} = ħ* ^{2}l(l* + 1) and of the projection of this momentum M

_{lz}=

*m*ħ onto the quantization axis

*z (*ħ is Planck’s constant

*h*divided by 2π), where the quantum number

*l*of the orbital angular momentum can assume any nonnegative whole value 0, 1, 2, … and the magnetic quantum number

*m*for a given

*l*can assume any whole value between –

*l*and +

*l*. The permitted values of the energy of a rotator are

*E*= ħ

^{2}

*l(l*+ l)/27; that is, they do not depend on

*m*. Thus, a (

*21*+ l)-fold degeneration of levels occurs by values of the projection of the angular momentum.

The rotator is important as an idealized model used to describe the rotational motion of molecules and nuclei. In particular, the rotator model is used to describe the motion of diatomic molecules in which the distance between the atoms is a quantity that varies comparatively little. The energy states of the rotation of such a molecule as a whole (the rotational spectrum of the molecule) are described by the formula for the energy of a quantum rotator.

V. G. VAKS